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This volume describes the observation, analysis and prediction of wind-generated waves in the open ocean, shelf seas, and coastal regions. It introduces observation techniques for waves, both in-situ and through remote-sensing, and defines the parameters that characterise waves.

We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of our analysis is to develop a sufficiently robust method, based on energy estimates and dispersive analysis, which allows us to deal simultaneously with strong singularities arising from time resonances in the applications of the normal form method and with nonlinear scattering. As a result, we are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of our analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.

The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.

This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, we can consider solutions such that the curvature of the initial free surface does not belong to The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. We first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then we use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.

Recent distributed acoustic sensing (DAS) experiments in ocean areas throughout the world have accumulated records for various wavefields. However, there are few tsunami records because tsunami observation depends on the DAS experimental period and its location. From continuous DAS records, we found tsunami signals at a frequency band of 5–30 mHz, which correspond to high‐frequency components of tsunamis and their propagation velocities differ from low‐frequency tsunamis. We estimated time series of the tsunami excitations at the source using the DAS records, which are consistent with those using records of ocean‐bottom absolute pressure gauges. Our study suggests that DAS records can be used for detecting tsunami propagations in the regions where other geophysical instruments are not available, and contribute to elucidating their excitation mechanisms. Plain Language Summary Using distributed acoustic sensing (DAS) techniques, various types of wavefields, such as earthquake and ocean waves, have been captured by submarine fiber optic cables. However, the recording of tsunamis has been limited, as their observation depends on the timing and location of the DAS experiments. On 8 October 2023, in southern Japan, changes in sea level attributable to tsunamis were detected by tide gauges. Continuous DAS records in southern Japan have enabled the capture of signals associated with these tsunamis. The observed signals exhibit frequency‐dependent propagation velocities, which correspond to infragravity waves. These are essentially deep water waves or ocean surface gravity waves, representing the high‐frequency components of tsunamis. Using the DAS records alone, we were able to estimate the time‐series of the tsunami generation at the source location. The features obtained from the time‐series were consistent with those from records of absolute pressure gauges on the seafloor deployed in southwestern Japan. Our findings demonstrate the utility of DAS records in detecting tsunami propagations and also elucidating excitation mechanisms of tsunamis. Key Points The countinuous records of our distributed acoustic sensing measuresment capture tsunami‐related signals The phase velocity dispersion of the obtained signals matches that of infragravity waves (high‐frequency tsunamis) The time‐series of the tsunami generation obtained by the cable data are consistent with those from nearby absolute pressure gauges

Waves in Oceanic and Coastal Waters describes the observation, analysis and prediction of wind-generated waves in the open ocean, in shelf seas, and in coastal regions with islands, channels, tidal flats and inlets, estuaries, fjords and lagoons. Most of this richly illustrated book is devoted to the physical aspects of waves. After introducing observation techniques for waves, both at sea and from space, the book defines the parameters that characterise waves. Using basic statistical and physical concepts, the author discusses the prediction of waves in oceanic and coastal waters, first in terms of generalised observations, and then in terms of the more theoretical framework of the spectral energy balance. He gives the results of established theories and also the direction in which research is developing. The book ends with a description of SWAN (Simulating Waves Nearshore), the preferred computer model of the engineering community for predicting waves in coastal waters.

Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the ‘phase-inversion’ method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the $n$ th-harmonic force scales with the $n$ th power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

Deep-water surface wave breaking affects the transfer of mass, momentum, energy and heat between the air and sea. Understanding when and how the onset of wave breaking will occur remains a challenge. The mechanisms that form unforced steep waves, i.e. nonlinearity or dispersion, are thought to have a strong influence on the onset of wave breaking. In two dimensions and in deep water, spectral bandwidth is the main factor that affects the roles these mechanism play. Existing studies, in which the relationship between spectral bandwidth and wave breaking onset is investigated, present varied and sometimes conflicting results. We perform potential-flow simulations of two-dimensional focused wave groups on deep water to better understand this relationship, with the aim of reconciling existing studies. We show that the way in which steepness is defined may be the main source of confusion in the literature. Locally defined steepness at breaking onset reduces as a function of bandwidth, and globally defined (spectral) steepness increases. The relationship between global breaking onset steepness and spectral shape (using the parameters bandwidth and spectral skewness) is too complex to parameterise in a general way. However, we find that the local surface slope of maximally steep non-breaking waves, of all spectral bandwidths and shapes that we simulate, approaches a limit of $1/\\tan ({\\rm \\pi} /3)\\approx 0.5774$. This slope-based threshold is simple to measure and may be used as an alternative to existing kinematic breaking onset thresholds. There is a potential link between slope-based and kinematic breaking onset thresholds, which future work should seek to better understand.